Seasonal Radiative Response


[This was originally posted in 2013 on Judith Curry’s site and was authored by CASF member, Steve McGee.  We have included it here as part of the CASF Archive.  Posted on December 26, 2013 | 169 Comments]

by Steve McGee

In science, one likes to have more examples than theories. – Dusan Djuric

Those words, spoken whimsically about cosmology, apply to climate science as well. The theory of the sensitivity of climate to the radiative SFCTforcing imposed by a doubling of carbon dioxide suffers from a lack of observed, repeatable examples. Paleo-climate studies carry with them the uncertainty of the proxy data and unmeasured assumptions on which they are based. Studies regarding the forcing from volcanoes and other transient events may not be repeatable for some time. However, Lindzen et. al. 1995 (link ) and Ramanathan and Inamdar in Frontiers of Climate Modeling, 2006 (link ) each have pointed out that the seasonal variation of earth temperature is quite large and possibly a surrogate for climate change. With this in mind, I set out to determine how the seasonal variation occurred in the CFSR data set ( described at this link, and data available at this link ), which I examined in a previous post Is earth in energy deficit? Because of some missing data, the following analyses exclude all observations from the year 1994.

The global average temperature variation, below, does indeed reflect a large signal. As described in the references, this variation stems from the fact that land has a much lower heat capacity than the oceans and that most of the earth’s land surface exists in the Northern Hemisphere. This arrangement amplifies the effect of the Northern Hemisphere seasonal cycle and dampens the effect of the  Southern Hemisphere seasonal cycle in the global mean surface temperature.


We can see this pattern more clearly in the global averages by month. Not only does the surface temperature vary, but so too does the outgoing longwave radiation.


Precipitable water is an absolute measure of water vapor in the atmosphere which also co-varies with surface temperature. This is consistent with water vapor feedback.


A correlation of all outgoing radiance versus temperature for all months yields the following plot. The darker shaded area represents a variance within 1 standard deviation. The lighter shaded area represents a variance within 2 standard deviations.


Each year of response becomes an individual example or experiment in how earth emits longwave radiation in response to surface temperature change. And by collating the number of years that the correlated response falls into specific ranges, we arrive at a rough indication of the frequency. Dividing 3.7 W/m^2, which is the assumed value of radiative forcing for a doubling of carbon dioxide, by the observed seasonal correlation of energy and temperature, results in the analogous temperature response. The error range indicated ( 1.6C to 4.6C ) is that of all the monthly data considered. The range of annual observed seasonal correlations is from 2.0C to 2.7C. The most frequent correlated response for the CFSR years was 2.5C.


By overlaying the CFSR seasonal response frequency over the chart ( at this link ) we can compare the seasonal response to the sensitivities indicated by climate models. ( the scale for seasonal response remains in years, not normalized frequency ).


Strengths and Weaknesses of this approach

There are number of strengths and weaknesses to using the seasonal response as an analog to climate change induced by greenhouse gasses. Strengths include: 1.) The large range of outgoing longwave radiation is around 6 W/m^2 which is considerably larger than the 3.7W/m^2 estimated to result from carbon dioxide doubling. 2.) The variation in the global mean, not just smaller regions. 3.) The repeatability of each year’s variation which creates a new example of radiative response 4.) The water vapor feedback and all other fast feedbacks are included in the variation.

Weaknesses include: 1.) The uncertainty inherent in re-analyses data set. However, one of the largest sources of error in re-analyses is the change in instruments which can introduce longer term trends. But because the seasonal data compares the averages per month, potential changes in data sets are smoothed. 2.) No shortwave feedbacks are included by examining only the seasonal OLR response to surface temperature while the climate models do include albedo feedback. This is lessened somewhat by recalling that albedo feedback is estimated to be the weakest feedback ( see Soden and Held at this link ). 3.) Perhaps most importantly, the very assymetry that produces the temperature fluctuation produces different patterns and distributions of temperature, jet streams, ITCZ, tropopause heights, and a many of other dynamic features of the atmosphere. The change from radiative forcing, from lesser forcing to greater forcing, integrated year round is a different distribution of response than the seasonal change we examine here from winter to summer and back to winter. These questions are beyond this look at the data, but would seem worth pursuing. It should also be pointed out that paleo-climate also has a different distribution than present climate – miles high ice-sheets where plains lie today, lower sea level, and so on.


There is much to consider here. Climate sensitivity is usually assessed with temperature as the dependent variable: ‘How much will surface temperature rise in response to a given radiative forcing?’ The meaning of the seasonal response is that outgoing longwave radiance is the dependent variable: ‘How much will outgoing radiance rise in response to surface temperature rising?’ In the longer term, these relationships are the same, for if a radiative forcing is imposed, heat will accumulate and raise the surface temperature which increases the OLR to the level at which heat accumulation stops.

The precipitable water values are not used in the simple correlation above, but I included the plot as a reminder that water vapor does appear to provide a feedback. The fact that the implied seasonal sensitivity of 0.65C per W/m^2 is greater than the Planck response indicates a net positive feedback. It is sometimes expressed that global warming will accelerate because positive feedbacks are lagging. The evidence in the seasonal response is that the largest identified feedback, water vapor, responds within a month – a fast feedback indeed.

In some ways, the seasonal response confirms current understanding of climate sensitivity. Hansen et. al. 2013 ( at this link ) find a paleo-climate sensitivity of 0.75C per W/m^2. The reciprocal of the observed seasonal correlation above yields 0.65C per W/m^2. And the range of uncertainty in the seasonal response ( 1.6C to 4.6C ) is quite similar to those suggested by the IPCC. On the other hand, the frequency of years of best seasonal correlation indicate a much less variable range than many models do for future climate. Further, the seasonal responses do not support the higher sensitivities indicated by some model runs.

Ultimately, Lindzen decided that the seasonal variation was not a ‘surrogate’ for ‘climate change’ within the constraints of the data set he was using. Perhaps ‘analog’ is a better description. The morphology of the variations are clearly different, but the strong global average variation and expected features make the seasonal response an important phenomenon worth further study.

Steve McGee has a bachelor of science degree in meteorology. His long career of software engineering includes the development of numerous defense related systems providing analysis and display weather and atmospheric effects. Steve’s previous post at Climate Etc. and at this site: